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As a teacher, Chayes is awful. All he does in class are ridiculously in-depth proofs that you'll never need to know. I can literally count on one hand the number of example problems he did in class, and most of those were ridiculously simple and didn't teach you anything.
That said, if you're capable of teaching yourself the material, his class doesn't have to be horrible. His midterms were pretty easy. The final, on the other hand, was soul crushingly difficult in comparison. Don't walk into it expecting a third midterm, because you'll screw up your grade. I should know; that's exactly what happened to me. Got A's on both midterms, ended up with a C in the class.
Chayes is eccentric to say the least, but he is by no means as bad as bruinwalk made him out to sound. At first, I didn't appreciate his teaching style, but as the quarter progressed, I began to appreciate his lectures. His lectures correlate very well with the text in the book. The information he presents in lecture is not contradictory or different from that in the text. He is concise about differentiating between the different approaches to a problem, such as different approaches taken by mathematicians, engineers, physicists, etc. Chayes is also very specific about his examples in lecture, for most end up being in the homework, which in turn end up on the midterms. His final was also pretty easy. He included a lot of leeway for screw ups. For example, the point cap was at 200 (so 200 was considered 100%) but there was well over 250 points available on the exam.
Perhaps the reason people dislike Chayes is because he is a shocker when it comes to first impressions. He wears the same black shoes, black pants, black shirt, black cardigan over the shoulder, and probably the same chalk all over his clothes from the day before (but he did wear a different jacket the last two lectures). Not only does he come out seeming like a weirdo in his own world, but he tends to make unique entrances (like running in through the front door yelling, I made it! or coming in late, saying MY tooth really hurts lol). His facial expression can be scary too, but I think that is just because he is focused on not screwing up on a stupid mistake and he constantly referring to his lecture notes. Most people were scared by this first impression, and add on the difficulty of his exam problems, and you have the reason for class drops.
BUT, stick with it after the first midterm, and you realize everything is like the homework. You also notice his lecture problems are the "hard ones" on the hw. You may even start appreciating his weird sense of humor, which I certainly did. His class was entertaining with the random chuckle here and there. Go to lecture, write down his examples, do the homework, and you will be fine.